The most common loss function employed in classification tasks is the categorical cross-entropy loss used in combination with softmax activation, which is often called SoftMax loss.
The basic hypothesis of this loss is that the final embeddings (aka. deep features) that result from this closed-set end-to-end training are sufficiently discriminative for open-set problems, i.e., when subjects from the test datasets differ from the people used during training.
Several extensions on top of this basic hypothesis were created over the years, including Center loss [1]}, which works in conjunction with the SoftMax loss to minimize the within-class distance of embeddings by learning a center for each class and penalizing the distance of features to the corresponding center [2]}.
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